GCF of 109/42, 106/689
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 109/42, 106/689 i.e 1/28938 easily. The following is the detailed procedure to determine the greatest common factor of fractions 109/42, 106/689.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 109/42,106/689?
Given fractions are 109/42,106/689
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 109/42,106/689, numerators are 109,106
Denominators are 42,689
The GCF of 109,106 is 1 .
LCM of 42,689 is 28938.
The greatest common factor of 109/42,106/689 = [GCF of 109,106]/[LCM of 42,689]= 1/28938
Therefore, the GCF of 109/42,106/689 is 1/28938.
To find the highest common factor of 109,106, we have to find the factors of both numbers and list the highest common factor.
The factors of 109 are 1, 109
The factors of 106 are 1, 2, 53, 106
The HCF of 109,106 is 1.
Lets's calculate GCF of 109,106
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 109,106 By Matching Biggest Common Factor Method
Now, list down the factors of 109
:1,109
Now, list down the factors of 106
:1,2,53,106
Greatest Common Factor
We found the factors 109,106 . The biggest common factor number is the GCF number.
So the greatest common factor 109,106 is 1.
Lets's calculate LCM of 42,689
Given numbers has no common factors except 1. So, there LCM is their product i.e 28938
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28938
Therefore, the GCF of Fractions 109/42,106/689 is 1/28938
Least Common Multiple of 42,689 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 42,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,689) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(42,689) x common factors =1 x 1 = 1
LCM(42,689) = ( 42 × 689 ) / 1
LCM(42,689) = 28938 / 1
LCM(42,689) = 28938
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 109/42, 106/689
1. What is the HCF of 109,106?
The HCF of 109,106 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 109/42, 106/689?
Answer: GCF of Numerators as per given numbers 109/42, 106/689 is
GCF of Numerators i.e. for 109,106 is 1
LCM of denominators i.e. for 42,689 is 28938.
Thus, GCF of Fractions is 1/28938.Finally, GCF of Fractions for 109/42, 106/689 is 1/28938.